What could Pythagoras’ greedy cup and a modern toilet possibly have in common?

Pythagorean Cup or the Greedy Cup was invented by Pythagoras so that wine drinking among workers could be moderated and the principles of justice could be highlighted for his students. Pythagoras’ concept was simple: Avidity for drinking should be limited! How? The clay cup empties in a magical way the minute it is filled with too much wine by the greedy imbider.

(image by Materialscientist)

But what is the limit? The cup must be filled up to a specific level, which is indicated with a line marked inside the cup. Provided that the liquid does not rise beyond the line, the cup can be used with no incident and the imbider can relax and enjoy the drink. However, if the cup is filled higher than the line, the wine starts to drain out of the bottom and the cup is soon completely empty!

(image by Nevit Dilmen)

pythagorean_cup03Wonder how this is possible? It’s just physics. The bowl of the cup has a column right in the centre positioned directly over the stem of the cup and over the hole at the bottom of the stem. A small open pipe runs from this hole almost to the top of the central column, where there is an open chamber. The chamber is connected by a second pipe to the bottom of the central column, where a hole in the column exposes the pipe to (the contents of) the bowl of the cup. When the cup is filled liquid rises up to the chamber at the top of the central column following Pascal’s principle of communicating vessels. As long as the level of the liquid does not rise beyond the level of the chamber, everything works fine and no one gets wet. If the level rises further, the liquid spills through the chamber into the first pipe and out the bottom.

For the record, modern toilets operate on the same principle of hydrostatic pressure: when the water level in the bowl rises high enough, a siphon is created, flushing the toilet.


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